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MOTION
93.
Pi to P2 along the tangent at P.    Therefore the average tangential acceleration is
Vz COS €2 — Vi COS €i
.
j.
/r=

This average approaches the actual tangential acceleration at P as Pi and P2 are made to approach P as a limit.   But
1ST
FIG. 57.
as these points approach P the angles *i and e2 approach zero as a limit and their cosines approach unity. Therefore the tangential acceleration at P is
By similar reasoning we obtain
>      """" ^2 sin €2 — v\ sin ei jn=. „f
for the average normal acceleration between Pi and P2. The actual normal acceleration at P is the limiting value of this expression as Pi and P2 approach P. But as these points approach P, vą and v% approach v, the velocity at P, while